Question #b5921

1 Answer
A08
Apr 9, 2017

Binding energy of a satellite is the energy which must be added to planet-satellite system to free the duo from their gravitational attraction.
If a satellite of mass m orbits a planet having mass M at a radius R_O with orbital velocity v, the total energy of the system is given by
E_"Total"=GPE+KE
=>E_"Total"=-(GMm)/R_O+1/2mv^2 .....(1)
where G is Universal Gravitational constant.

We know that for circular motion
F_"Centripetal" = (m v^2) / R_O
and force of gravity is
F_"grav" = ( G Mm ) / R_O^2

As the system is in equilibrium, the centripetal force must be balanced by the gravitational attraction force between the two. Therefore we get
(m v^2) / R_O= ( G Mm ) / R_O^2
=>v^2 = ( G M ) / R_O .....(2)

Inserting this value in (1) we get
E_"Total"=-(GMm)/R_O+1/2m( ( G M ) / R_O)
E_"Total"=-1/2(GMm)/R_O ....(3)

When the planet-satellite duo are free from each others gravitational pull, (implies that R_O=oo), we have

E_"Total"+BE=0
=>BE=-(E_"Total")

Using (3) we have
BE=1/2(GMm)/R_O

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